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Cheat sheet

ACT Math cheat sheet

A condensed reference for the formulas, graph-reading rules, and must-know facts most worth reviewing before exam day.

Memorize these (no formula sheet!)

  • Slope m = (y2 − y1)/(x2 − x1); line y = mx + b.
  • Distance = √[(x2 − x1)² + (y2 − y1)²]; Midpoint = ((x1+x2)/2, (y1+y2)/2).
  • Quadratic formula x = [−b ± √(b² − 4ac)] / 2a.
  • Area: triangle ½bh, circle πr², rectangle lw, trapezoid ½(b₁+b₂)h. Circumference 2πr.
  • Volume: box lwh, cylinder πr²h. Pythagorean a² + b² = c².

Algebra & numbers

  • Exponents: aᵐ·aⁿ = aᵐ⁺ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁻ⁿ = 1/aⁿ, a⁰ = 1.
  • Factor quadratics and use the difference of squares a² − b² = (a−b)(a+b).
  • Percent change = (new − old)/old × 100; 'of' means multiply.
  • Solve proportions by cross-multiplying; keep units consistent.
  • FOIL to expand binomials; combine like terms carefully with signs.

Geometry & trig

  • Angles: a straight line = 180°, a triangle's angles sum to 180°, a full circle = 360°.
  • Special right triangles: 45-45-90 sides x : x : x√2; 30-60-90 sides x : x√3 : 2x. Triples 3-4-5, 5-12-13.
  • SOH-CAH-TOA: sin = opp/hyp, cos = adj/hyp, tan = opp/adj.
  • Similar triangles have proportional sides; parallel lines cut by a transversal make equal corresponding/alternate angles.
  • Circle: central angle, arc, and sector all scale with the fraction of 360°.

Data, stats & pacing

  • Mean = sum ÷ count; median = middle value; mode = most frequent.
  • Probability = favorable ÷ total; multiply independent events, add mutually exclusive ones.
  • Read every chart's axes and units before computing.
  • Answer easy early questions fast, flag the slow ones, and never leave a blank (no penalty).
  • If stuck, plug in the answer choices or pick smart numbers.

Practice this first: Algebra - The core of the section — linear and quadratic equations, expressions, and functions appear throughout.

Now put it to work - practice ACT Math free

Reviewing the sheet is step one. Passers are usually hitting about 70-80% on realistic practice before test day, so the fastest way to know you are ready is to start answering real questions.